The research was "a landmark in our fight against cancer", the Nobel Assembly of Sweden's Karolinska Institute said in announcing the award.
The institute added that therapies based on Prof Honjo's discovery "proved to be strikingly effective in the fight against cancer".
According to MD Anderson, Allison's crucial insight was to block a protein on T cells that acts as a brake on their activation, freeing the T cells to attack cancer.
Unlike more traditional forms of cancer treatment that directly target cancer cells, Allison and Honjo figured out how to help the patient's own immune system tackle the cancer more quickly.
One of Carter's treatments was a drug that blocked the immune-cell "brake" studied by Honjo. "We are delighted that it was positively evaluated", said Shinsuke Amano, head of the Japan Federation of Cancer Patient Groups.
In 2014, the FDA approved the drugs Keytruda and Opdivo, which inhibit another checkpoint molecule, PD-1, for the treatment of metastatic melanoma. Releasing the brake allowed immune cells to attack tumors, he found.
"I'm honored and humbled to receive this prestigious recognition", Allison said.
Also attending the news conference was his 75-year-old wife, Shigeko, who said, "I have taken upon myself the job of supporting my husband, so I am very happy that he received the Nobel Prize".
A professor at the Unviersity of Texas MD Anderson Cancer Center was among two people Monday who were awarded the Nobel Prize in Medicine. After pondering what career to pursue - diplomat, lawyer or doctor - Honjo entered the Faculty of Medicine at Kyoto University in 1960 and moved on to the graduate course.
These and rival drugs from Roche, AstraZeneca, Pfizer and Sanofi now offer new options for patients with melanoma, lung and bladder cancers.
He said Allison's work a decade ago "really opened up immunotherapy" as a fifth pillar of cancer treatments, after surgery, radiation, chemotherapy and precision therapy. Honjo is credited with discovering PD-1 and also recognising the importance of blocking its function as a potential cancer treatment. "I would like to keep on doing my research.so that this immune treatment could save more cancer patients", he said.
But new studies suggest combining a therapy targeting both CTLA-4 and PD-1 can be even more effective, particularly in patients with melanoma. American James Allison and Japanese Tasuku Honjo were awarded the honourable prize by the award-giving body. Experts previously thought that metastasis, when the cancer spreads to other organs and tissues, was untreatable, the Nobel committee's press release explains.
Macedonia PM urges ratification of referendum result
That was far short of the participation threshold of 50 per cent, even though 91 per cent of those who voted supported the deal. Zaev cast his ballot in the southeastern town of Strumica and called on his fellow citizens to ensure a strong turnout.